Bohr Hamiltonian with a potential having spherical and deformed minima at the same depth

A solution for the Bohr-Mottelson Hamiltonian with an anharmonic oscillator potential of sixth order, obtained through a diagonalization in a basis of Bessel functions, is presented. The potential is consid- ered to have simultaneously spherical and deformed minima of the same depth separated by a barrier (a local maximum). This particular choice is appropriate to describe the critical point of the nuclear phase transition from a spherical vibrator to an axial rotor. Up to a scale factor, which can be cancelled by a corresponding normalization, the energy spectra and the electromagnetic E2 transition probabilities depend only on a single free parameter related to the height of the barrier. Investigations of the numerical data revealed that the model represents a good tool to describe this critical point.

SOLUTION FOR THE EIGENENERGIES OF SEXTIC ANHARMONIC OSCILLATOR POTENTIAL V(x)=A6x6+A4x4+A2x2

In this paper a study of the sextic anharmonic oscillator potential V(x)=A6x6+A4x4+A2x2 (A6≠0) using the asymptotic iteration method is presented. We calculate the eigenenergies for different excited states. The used method works very well for this potential and in fact one is able to obtain high accuracy with the asymptotic iteration method. A comparison between our results with other methods found in literature is presented.